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The Triad Inversion Calculator is a specialized tool designed to simplify the process of identifying and applying the three primary inversions of musical triads: root position, first inversion, and second inversion. By inputting the root note of any triad, users can instantly receive information about the notes that constitute the triad in its different inversions. This facilitates a deeper understanding of chord structures and their variations, making it easier for musicians to experiment with harmony and chord progression in their compositions or performances.

## Formula of Triad Inversion Calculator

The underlying mathematics of triad inversions are straightforward yet pivotal for musicians. Here, we break down the formulas for each triad inversion:

#### Root Position Triad: The root note is at the bottom.

```Root Position: [Root, Third, Fifth]

Variables:
Root: The root note of the triad.
Third: The note a third above the root.
Fifth: The note a fifth above the root.
```

#### First Inversion Triad: The third of the chord is at the bottom.

```First Inversion: [Third, Fifth, Root an octave higher]

Variables:
Third: The note a third above the root.
Fifth: The note a fifth above the root.
Root an octave higher: The root note of the triad placed one octave higher.
```

#### Second Inversion Triad: The fifth of the chord is at the bottom.

```Second Inversion: [Fifth, Root an octave higher, Third an octave higher]

Variables:
Fifth: The note a fifth above the root.
Root an octave higher: The root note of the triad placed one octave higher.
Third an octave higher: The third of the triad placed one octave higher.
```

## Table for General Terms

This table represents major triads in their root position and their inversions.

## Example of Triad Inversion Calculator

Let’s consider a C Major triad to see how the calculator simplifies the inversion process:

• Root Position: C-E-G
• First Inversion: E-G-C (C is an octave higher)
• Second Inversion: G-C-E (C and E are an octave higher)

This practical example demonstrates the ease with which musicians can explore different chord voicings using the calculator.